pubs.acs.org/Langmuir © 2009 American Chemical Society
Additional Support for a Revised Gibbs Analysis Fredric M. Menger,* Lei Shi, and Syed A. A. Rizvi Department of Chemistry, Emory University, 1515 Dickey Drive, Atlanta, Georgia 30322 Received November 20, 2009. Revised Manuscript Received December 1, 2009 Gibbs-determined areas of >60 A˚2/molecule for many common surfactants cause rather small surface tension reductions when measured on a Langmuir film balance. This is inconsistent with an air/water interface being saturated throughout the steep linear decline in plots of surface tension versus ln [surfactant]. In support for a gradually populating interface in the linear region, we have found that sodium docosanyl sulfate lowers the surface tension by only 7 mN/m when compressed to 50 A˚2/molecule. When docosanyltrimethylmmonium bromide is compressed to 65 A˚2/ molecule, the surface tension is lowered about 15 mN/m as compared to a 30-40 mN/m drop occurring within the range of typical Gibbs analysis. Saturation of the interface is often obscured by competitive micelle formation that levels the surface tension versus ln [surfactant] plot before saturation has a chance to do so.
The Gibbs analysis of surface tension at the air/water interface postulates that the air/water interface is entirely saturated with adsorbent throughout region B of Figure 1, a region where the surface tension experiences a steep linear decline with ln [surfactant]. This postulate allows the calculation of area-permolecule at the interface via eqs 1 and 2 (where Γ = the surface excess; c = bulk concentration; γ = surface tension; dγ/d(ln c) = the slope of line B; and N = Avogadro’s number). Γ ¼ -ðdγ=d ln cÞ=ðnRTÞ
ð1Þ
area ¼ 1016 =ðNΓÞ
ð2Þ
Saturation throughout region B is required here because if the interface were not saturated, and its occupancy were thus continually changing with concentration, calculation of a single area would obviously make no sense. The Gibbs analysis has been a stalwart component of colloid chemistry; hundreds of areas have been published in papers and textbooks using this approach.1 We recently published what some may consider a blasphemous re-evaluation of the above Gibbs analysis.2 On an intuitive level, we wondered why the surface tension should remain relatively constant in region A but then begin its precipitous decline only after saturation is ostensibly reached at the beginning of region B. In other words, it seemed strange that the surface tension is hardly affected by molecules populating the interface and yet the surface tension decreases when molecules do not further adsorb. The large surface tension change in region B has been explained (rather vaguely in our view) by an “increased activity of the surfactant in the bulk phase rather than at the interface.”1 We argued for an alternative mechanism in which the surface tension decline in region B arises from a continuously increasing occupancy of the interface. In contrast to the Gibbs analysis, the mechanism seems to have a straightforward “cause and effect” appeal. Of course, a variable region B implies that the Gibbs calculations of molecular areas have no physical basis. *To whom correspondence should be addressed. E-mail: menger@ emory.edu. (1) Rosen, M. J. Surfactants and Interfacial Phenomena, 3rd ed.; Wiley: Chichester, U.K., 2004; pp 65-80. This reference contains a 16-page listing of surfactant areas. (2) Menger, F. M.; Shi, L.; Rizvi, S. A. A. J. Am. Chem. Soc. 2009, 131, 10380.
1588 DOI: 10.1021/la9043914
Two questions immediately arise from our mechanism. The first deals with why the surface tension changes very little in the low-concentration region A of Figure 1. In our view, the adsorption of surfactants to the interface is cooperative (for the same reason that micelle formation is cooperative). This means that there should be an induction period followed by a rapidly developing adsorption at the interface. These phenomena are represented by region A and region B, respectively. Further details of the cooperativity aspect of interfacial adsorption can be found in our previous publication.2 The second question relates to the issue of saturation. If saturation is not present within region B, then when does it occur? This is difficult to answer because we believe that micelle formation usually obscures interfacial saturation. Thus, surface tension versus ln [surfactant] plots level off (often between 30 and 40 mN/m) owing to micelle formation (region C, Figure 1). Surfactant molecules prefer joining the micelles over entering an unsaturated interface. If it were not for micelle formation, region B would continue its downward journey and then level off at the saturation point rather than at the critical micelle concentration (CMC). We have actually found a rare case of a mixed-micelle system in which saturation of the interface occurs prior to micelle formation.2 This was apparent from the fact that the break in the surface tension versus ln [conc] plot occurs far below the breaks derived from two “bulk” CMC measurements (NMR and conductivity). The simplest explanation is that surface tension detected interfacial saturation, whereas the NMR and conductivity detected micelle formation occurring at a higher concentration. More substantial evidence was needed to support our model. Toward this end, we used a Langmuir film balance to obtain the surface tension versus area-per-molecule plot for an insoluble hexadecanol monolayer. A Langmuir film balance has the advantage of allowing direct measurements of molecular areas.3 The surface tension remained constant at the water value of 72 mN/m all the way from 60 A˚2/molecule down to 28 A˚2/molecule. However, a variety of single-chained surfactants have, as derived (3) Moroi, Y. in Croat. Chem. Acta 2007, 80, 381 argues that soluble surfactant films are concentrated as aggregates at some distance beneath the air/water interface. If this is true, then it greatly complicates our comparison of soluble and insoluble films at the air/water interface. Our results are predicated on the assumption that both types of film have the ionic headgroups immersed in the water and the hydrocarbon tails projecting into the air.
Published on Web 12/04/2009
Langmuir 2010, 26(3), 1588–1589
Menger et al.
Figure 1. Three regions of a typical surface tension versus ln [surfactant] plot. The Gibbs approach uses the linear region B to calculate molecular areas under the assumption that the interface is saturated in this region.
by the Gibbs approach, areas above 60 A˚2/molecule (e.g., 65 and 64 A˚2/molecule for C12H25SO3-Naþ and C18H37N(CH3)3þBr-, respectively).3 This means that when the Gibbs method is applied to a steeply declining surface tension plot, the area thus obtained corresponds, according to our data,2 to a zero surface tension change, an obvious inconsistency. Stated in another way, when adsorbed molecules are each allowed >60 A˚2/molecule at the air/ water interface, the interface is too sparsely populated to lower the surface tension appreciably, in direct conflict with the Gibbs construct. There exists a valid criticism of our previous work.2 We originally used hexadecanol for our experiments because the common ionic surfactants are too water-soluble for Langmuir balance studies. Since it would have been preferable to make comparisons using ionic monolayer films, we now report Langmuir balance studies on ionic surfactants with chains sufficiently long to form stable monolayers. Thus, surface tension versus area-per-molecule plots are given below for C22H43OSO3-Naþ (Figure 2) and C22H43N(CH3)3þ Br- (Figure 3). It is seen that C22H23OSO3-Naþ displays only a 7 mN/m drop in surface tension when the monolayer is compressed to 50 A˚2/molecule, as compared to a 30-40 mN/m drop occurring within the range of a typical region B. Similarly, at 64 A˚2/molecule (the Gibbsdetermined area for a film of C18H37N(CH3)3þBr-), the surface tension for C22H43N(CH3)3þ Br- is 57 mN/m, a value much greater than the lower surface tensions encompassed by region B. In summary, we have shown that molecular areas calculated by applying the Gibbs equation to region B are based on an unconfirmed assumption, namely that the interface is already saturated when the surface tension first begins its precipitous linear decline. In order to achieve large surface tension reductions (typically
Langmuir 2010, 26(3), 1588–1589
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Figure 2. Plot of surface tension versus area/molecule for an insoluble monolayer of C22H45SO4-Naþ.
Figure 3. Plot of surface tension versus area/molecule for insoluble monolayer of C22H45N(CH3)3þBr-.
from 72 mN/m to 30-40 mN/m), the interface must be packed far more tightly than generally deduced from the Gibbs-obtained areas. Thus, Gibbs areas of >60 A˚2/molecule for many common surfactants produce rather small surface tension reductions when measured on a Langmuir film balance. Our alternative model postulates that the adsorbent progressively fills the interface in region B, thereby explaining the large surface tension decrease in this region. Saturation often goes unobserved because competitive micelle formation levels the surface tension versus ln [surfactant] plot before saturation has a chance to do so. Supporting Information Available: Experimental details. This material is available free of charge via the Internet at http://pubs.acs.org.
DOI: 10.1021/la9043914
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